A Note on the generating function of p-Bernoulli numbers

TL;DR

This paper employs analytic combinatorics to provide a direct proof of the closed-form generating function for p-Bernoulli numbers, enhancing understanding of their mathematical properties.

Contribution

It offers a novel, direct proof of the generating function for p-Bernoulli numbers using analytic combinatorics, which was not previously established.

Findings

Closed-form generating function for p-Bernoulli numbers derived

Analytic combinatorics techniques applied successfully

Provides a new proof method for Bernoulli-related sequences

Abstract

We use analytic combinatorics to give a direct proof of the closed formula for the generating function of $p$-Bernoulli numbers.